Math 120 MyMathLab Homework chp 1-3
Explain why the speed of the Earth makes sense. Choose the correct answer below.
speed= distance/time= 25,000 miles/24hours
Explain how we can use comparisons to put numbers in perspective. Give an example. Choose the correct answer below
Comparison allows numbers to be put in perspective by relating them to understandable values. The amount of electricity a power plant produces can be compared to the number of homes it can supply.
What is the purchasing power of $1 in 1980 in terms of 2011 dollars?
$2.73
The common fraction for 4.091
4091/1000
6.1 billion in scientific notation is
6.1x10^9
A toll collector on a highway receives $8 for buses and $5 for sedans. At the end of a 3-hour period, she collected $208. How many buses and sedans passed through the toll booth during that period? List all possible solutions.
6B 32S 1B 40S 11B 24S 16B 16S 21B 8S 26B 0S
The number of different sevenseven-character passwords that can be made with 26 letters and 10 numerals is approximately 78 billion.
7.8x10^10
What is energy? List three common units of energy. Under what circumstances do the different units tend to be used?
Energy is what makes matter move or heat up.
What is a second way to use percentages?
Percentages can be used to describe a change in something. For example, the cost of milk rose 5% within the past month.
At the end of a year, the gross debt of a country stood at about $23 trillion. Express this amount in dollars per person, assuming that the population of the country is about 292 million.
The gross is about $78800 per person
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 6.7 cubic feet of water weigh in pounds? In tons?
The weight in pounds is approximately 417.5 lb. (Round to the nearest tenth as needed.) The weight in tons is approximately 0.21 ton(s). (Round to the nearest hundredth as needed.)
The decimal form of 1/10 (Round to the nearest thousandth as needed.)
.1
convert the following fractions to decimal form.
1/10 is 1 2/9 is .222 5/11.is .455
For such a test, what is a false negative?
A false negative would be when an athlete that is using a banned substance tests negative for banned substances.
3D What is an index number? Briefly describe how index numbers are calculated and what they mean.
An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time or place is the reference value. The index number at any other time or place is given by index number =value/reference value×100.
Identify the conclusion. Choose the correct answer below.
I believe that vaccines cause autism.
Which of the following best summarizes the strategic hint "Do not spin your wheels" and provides an example of the meaning?
Often the best strategy in problem solving is to put a problem aside for a few hours or days. For example, if you are struggling with a problem involving long division with polynomials, set it aside and come back to it in a few hours.
The relative change is the size of the absolute change in comparison to the reference value and can be expressed as a percentage.
RC=absolute chg/reference value x 100%
Reuben says, "Two days ago I was 20 years old. Later next year, I will be 23 years old." How is this possible?
Reuben spoke on January 1 and was born on December 31.
Each of ten large barrels is filled with golf balls that all look alike. The balls in nine of the barrels weigh 1 ounce and the balls in one of the barrels weigh 2 ounces. With only one weighing on a scale, how can you determine which barrel contains the heavy golf balls?
Select one ball from the first barrel, two balls from the second barrel, and so on, up to ten balls from the tenth barrel to find the weight of a specific number of balls in a specific barrel.
How much will a person pay for 14.7 pounds of bananas at a price of $2.41 per pound?
The price the person will pay is 35.43 dollars. (Round to the nearest cent.)
What is the speed of the Earth?
The speed of the Earth is 1041.7 miles per hour.
A woman is traveling with a wolf, a goose, and a mouse. She must cross a river in a boat that will only hold herself and one other animal. If left to themselves, the wolf will eat the goose and the goose will eat the mouse. How many crossings are required to get all four creatures across the river alive?
To get all four creatures across the river alive, 7 crossings are required.
Will is 28% taller than Wanda, so Will's height is ____% of Wanda's height.
Will's height is 128% of Wanda's height.
Identify the units of the following quantities. State the units mathematically and in words. Your average speed on a long walk, found by dividing distance traveled in milesmiles by time elapsed in minutes What are the units mathematically?
mi/min
Five books of five different colors are placed on a shelf. The gold book is placed between the gray and brown books, and these three books are consecutive. The pink book is not leftmost on the shelf and the brown book is not rightmost on the shelf. The orange book is separated from the brown book by two books. If the pink book is not next to the orange book, what is the complete ordering of the books?
orange, gray, gold, brown, pink
Evaluate the following expressions. 2/5 x 5/9. 1/4 + 5/8
2/9 7/8
d. What is your average speed for the round trip?
The average speed for the round trip is about 3 miles per hour.
Identify the units of the following quantities. State the units mathematically and in words. Your average speed on a long walk, found by dividing distance traveled in milesmiles by time elapsed in minutes.
mi/min
To add numbers expressed in scientific notation, rewrite each number in ordinary notation and add the rewritten numbers. Then rewrite the sum in scientific notation. Rewrite each addend in ordinary notation. (3x10^9)+(5x10^8)=
3,000,000,000+500,000,000=3,500,000,000 Rewriting the sum in scientific notation shows 3.5x10^9
Rewrite the following statement using a number in scientific notation. My new music player has a capacity of 390 gigabytes. (Recall that giga means billion.)
My new music player has a capacity of 3.9x10^11
Choose the best explanation for why the fallacy is deceptive.
The conclusion is based on a personal allegation and a distortion of someone's words or beliefs.
b. Briefly describe how the stated fallacy occurs in the argument.
The premise is stated according to a lack of evidence of the opposite of the conclusion.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. If John earns 20% more than Mary does, then Mary must earn 20% less than John does.
The statement does not make sense because if John earns 20% more than Mary, then Mary must earn approximately 16.7% less than John does.
To divide numbers expressed in scientific notation, start by rewriting the expression so that the powers of 10 are in one group and the other numbers are in the second group. Then divide the groups separately. (9x10^17)/(3x10^11)= 9/3x10^17/10^11
Simplify the first factor. 3x10^6 To divide powers of 10, subtract the second exponent from the first. Simplify the second factor
Compare A and B in three ways, where A=1.61 million is the 2012 population of city X and B=2.9 million is the 2012 population of city Y. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.
a. The ratio of A to B is .55. b. The ratio of B to A is 1.81
b. How long did you spend walking home?
1.5 HOURS
Evaluate the following expressions.
1/3+2/3+2/9=37/18 2/3×42/5×10/7=8
Express the given percentage as a reduced reduced fraction and as a decimal. 40% What is the reduced fraction form of 40%?
2/5
b. Give numerical evidence to support the claim that college B has a better team than college A. Choose the correct answer below.
A. College B won about 62.5% of the games they played, whereas college A only won about 48.9% of the games they played.
1 decimeter on the map represents 1 meter on the ground.
The scale ratio is 1 to 10
A woman is traveling with a wolf, a goose, and a mouse. She must cross a river in a boat that will only hold herself and one other animal. If left to themselves, the wolf will eat the goose and the goose will eat the mouse. How many crossings are required to get all four creatures across the river alive?
To get all four creatures across the river alive, 7 crossings are required.
Evaluate the following expressions. a. 2/5×5/9. b. 1/4₊5/8
a 2/9 b. 7/8
What are the units in words?
miles per minute
A thin tube stretched across a street counts the number of pairs of wheels that pass over it. A vehicle classified as type A with eighteight axles registers eight counts. A vehicle classified as type B with nine axles registers ninenine counts. During a 4-hour period, a traffic counter registered 37 counts. How many type A vehicles and type B vehicles passed over the traffic counter? List all possible solutions.
1A 41B 10A 33B 19A 25B 28A 17B 46A 1B 27A 9B
it cost $33 to fill a gas tank in 1960, how much of the same tank could be filled with $33 in 1980?
Divide the index numbers for the two years to find how much more expensive gas was in 1960, compared to 1980. About 0.25 of the same tank could be filled.
Which player had the higher batting average in the second half of the season?
Josh
Suppose a patient in the general population tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure with the overall incidence rate of the disease.
The chance of the patient having HIV is 5%, compared to the overall incidence rate of 0.3%. (Type an integer or decimal rounded to the nearest tenth as needed.)
Describe how units can help to check the answers and solve problems. Give examples.
Consider a box with the side lengths in inches. The volume of the box would be calculated in cubic inches. The key word "cube or cubic" in this context means that the unit inches is raised to the third power. The mathematical symbol to represent the unit of the volume of the box is "in ^3."
b. What is the conclusion? Choose the correct answer below.
People who exceed the speed limit are criminals.
Use estimation to make the following comparison. Which is greater, the amount the average person spends in a month on coffee or the amount the average person spends in a month on gasoline?
The amount a person spends on gasoline in a month is greater.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Mathematics requires precision, so approximations should never be used.
The statement does not makes sense because most real problems involve approximate numbers.
What are units? Describe how units can help to check answers and solve problems. Give examples. What are units?
Units are words that describe what is being measured or counted.
Express the given percentage as a reduced fraction and a decimal. 475%
19/4 4.75
Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Whether it's a problem in mathematics or something else, I always find it's best to complete the work by looking back to check, interpret, and explain my solution.
Makes sense
Evaluate the following expressions.
10¹⁸/10¹²=10⁶ 10¹+10⁰=11 10³+10⁻²=1000.010³-10²=900
Convert the following fractions to decimal form. (Round to the nearest thousandth as needed.)
3/5=0.6
Convert the following temperatures from Fahrenheit to Celsius or vice versa.
C=F-32/1.8 F=1.8C+32 25°F=-3.9°C 85°C=185°F -15°C=5°F
How would you verify the detection rates?
Divide the total number of true positives by the total number of patients.
Which player had the higher overall batting average for the season?
Jude had the higher overall batting average for the season.
d. Consider a patient in the general population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.
Of the patients in the general population with HIV, 88.3% test positive. Of the patients in the general population who test positive, 5% have HIV.
c. Which claim do you think makes more sense? Why?
The claim in part B makes more sense because it is based on the total number of games played.
Explain how a state could score lower in both categories and still have a higher overall average. Choose the correct answer below.
The state could have a higher percentage of students in the category that had the highest average score
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Baggage screening machines are 98% accurate in identifying bags that contain banned materials. Therefore, if the screening shows a bag that contains banned materials, then it almost certainly does
The statement does not make sense because, depending on the proportion of true positives to total positives, the actual percentage of bags that show banned materials and actually have banned materials could be quite low.
According to the video,http://mediaplayer.pearsoncmg.com/assets/UUM7B_1a_ex5 what does the argument suggest?
There are only two types of Americans: patriotic ones who support the military and unpatriotic ones who don't.
Briefly describe the Understand-Solve-Explain approach to problem solving, giving examples of things that should be considered in each step. What is the "Understand" step of this part of the problem solving approach?
The "Understand" step is to think about what the problem asks to be determined.
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and identify the type of fallacy it represents. The Congressperson is a member of a national firearms club, so I'm sure she will not support a ban on rifles.
Premise: The Congressperson is a member of a national firearms club. Conclusion: I'm sure she will not support a ban on rifles.
Complete the following sentence with a power of ten greater than 1. A liter is _______ times as large as a microliter.
A liter is 10⁶ times as large as a microliter.
Briefly explain why a positive result on a screening test for a disease does not necessarily mean that a patient has the disease.
The test may have produced a false positive.
What is the decimall form of 40%?
.40
What is the speed of the Earth?
1041.7 miles per hour.
Express the given decimal as a percentage and as a fraction 0.05
5% 1/20
What is logic? Briefly explain how logic can be useful.
Logic is the study of the methods and principles of reasoning. It can be useful in providing strong support for conclusions, and to help identify errors in reasoning, or fallacies.
According to the video, after what step could we conclude the claim to be false? Choose the correct answer below. A. Step 2: Check the date. B. Step 5: Don't miss the big picture. C. Step 4: Watch for hidden agendas. D. Step 1: Consider the source. E. Step 3: Validate accuracy.
Step 3: Validate accuracy.
Evaluate the following expressions.
10⁸×10⁷=10¹⁵ 10⁹x10⁻³=10⁶ 10⁴/10²=10² 10¹²x/10⁻⁴=10¹⁶
Convert the following temperatures from Kelvin to Celsius or vice versa.
C=K-273.15 K=C+273.15 30K=-243.15°C 230K=-43.15°C 30°C=303.15K
Complete the following sentence with a power of ten greater than 1. A terameter is _______ times as large as a meter.
A terameter is 10¹² times as large as a meter.
a. Give numerical evidence to support the claim that college A has a better team than college B. Choose the correct answer below.
A. College A won about 34.5% of their home games and about 75% of their away games, whereas college B only won about 32.1% of their home games and about 73.7% of their away games.
Which of the following best summarizes the strategic hint "Try alternative patterns of thought" and provides an example of the meaning?
Avoid patterns of thought that tend to suggest the same ideas and methods. Instead, approach problems with an openness that allows new ideas and solving methods. For example, when solving a problem that requires more thought, a moment of insight may be useful and make the problem easier to solve
Describe how units can help to check the answers and solve problems. Give examples.
Consider a box with the side lengths in inches. The volume of the box would be calculated in cubic inches. The key word "cube or cubic" in this context means that the unit inches is raised to the third power. The mathematical symbol to represent the unit of the volume of the box is "in³."
The average price of a domestic airline ticket increased from $269 in 1994 to $411 in 2016. Use the table to the right to complete parts (a) and (b) below. a. Calculate the relative change in price from 1994 to 2016 and compare this change to the overall rate of inflation as measured by the Consumer Price Index.
Domestic airline ticket prices increased by 53%. (Round to the nearest integer as needed.) The overall rate of inflation was 662%. (Round to the nearest integer as needed.) The change in domestic airline ticket prices was less than the overall rate of inflation.
Explain why the argument is deceptive. Choose the correct answer below.
The argument is deceptive because it attempts to create a link between vaccines and autism. The premise of the argument does not fully support the conclusion.
Write each of the following as a common fraction.
The common fraction for 4.25 is= 17/25 0.65=13/20 0.006=3/500 2.26=54/25 8.5=17/25 4.091=4091/1000 0.00077/1000
Explain why the argument is deceptive. Choose the correct answer below.
The conclusion is drawn from an inadequate number of cases and uses ignorance about the truth to conclude the opposite.
Write out the three steps of the Understand-Solve-Explain process when answering the following question. How fast does Earth rotate? Note that in one full rotation of Earth, a point on the equator travels about 25,000 miles in 24 hours. What is the unknown in this problem?
The speed
Decide whether the following statement makes sense or does not make sense. Explain your reasoning. I drove at a speed of 35 miles for the entire trip.
The statement does not make sense because miles is not a unit of speed.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The Republicans claim the tax cut benefits everyone equally, but the Democrats say it favors the rich. Clearly one side is lying.
The statement does not make sense because the two parties are using selective truth. The Republicans are masking the change, where the Democrats are focused on the absolute change, but ignoring the fact that the wealthy pay most of the taxes.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Despite the fact that the new drug lowered blood pressure more than the old drug did in both the men and the women in the study, an overall analysis shows that the old drug was actually more effective.
The statement makes sense because there is no information given about the sampling method or about how the trials of the test were divided.
Consider the following exam question and student solution. Determine whether the solution is correct. If it is not correct, write a note to the student explaining why it is wrong and give a correct solution. Exam question: You can buy a 34-pound bag of flour for $6or you can buy a 1-pound bag for $0.39. Compare the per pound cost for the large and small bags. Student solution: The large bag price is 34÷$6=$5.67 per pound, which is much more than the 39¢ per pound price of the small bag. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The student's solution is incorrect. The student's division gives an answer with units of pounds per dollar, but he should seek an answer in dollars per pound. The answer in dollars per pound is $.18 per pound, which is less than the $0.39 per pound for the smaller bag. (Round to the nearest cent as needed.)
Complete parts (a) through (c) below. a. A warehouse is 65 yards long, 32 yards wide, and 7 yards high. What is the area of the warehouse floor? If the warehouse is filled to half its height with tightly packed boxes, what is the volume of the boxes? b. A room has a rectangular floor that measures 27 feet by 13 feet and a flat 8-foot ceiling. What is the area of the floor and how much air does the room hold? c. A grain silo has a circular base with an area of 155 square feet and is 23 feet tall. What is the total volume?
a) The area of the warehouse floor is 2080yd2. (Type an integer or a decimal.) The volume of the boxes in the warehouse is 7280^2yd cubed . b. The area of the floor is 351^2 ft squared . The amount of air the room can hold is 2808ft^3 cubed . c. The volume of the grain silo is 3565^3ft cubed .
Suppose that a test for performance-enhancing drugs is 8080% accurate (It will correctly detect 8080% of people who use such drugs and will correctly detect 8080% who do not). Suppose that, 22% of the 2000 athletes in a major meet have actually taken performance-enhancing drugs, and all athletes are given the drug test. Complete parts (a) through (c) below. Users Non-Users Total Test finds drug use 3232 392392 424424 Test finds no drug use 88 15681568 15761576 Total 4040 19601960 2000
a. Verify that the entries in the table above agree with the information given. Explain each entry. The table shows a total of 20002000 athletes tested. The total number of athletes using performance-enhancing drugs is 4040, which is 22% of the total athletes tested. The test correctly detected 3232 athletes using, which is 8080% of the total athletes using. The test correctly detected 15681568 athletes not using, which is 8080% of the total athletes not using. Therefore, the table agrees with the information given. (Type whole numbers.) b. How many athletes in total were accused of using performance-enhancing drugs? Of these, how many were using and how many were not? What percentage of those accused of using were falsely accused? There were 424 athletes in total that were accused of using performance-enhancing drugs. (Type a whole number.) Of those accused, 3232 athletes were using. (Type a whole number.) Of those accused, 392392 athletes were not using. (Type a whole number.) The percentage of those accused of using who were falsely accused is 92.592.5%. (Type an integer or decimal rounded to one decimal place as needed.) c. How many athletes in total are cleared of using performance-enhancing drugs? Of these, how many were actually using the drugs? What percentage does this represent of those cleared? There were 15761576 athletes cleared of using performance-enhancing drugs. (Type a whole number.) Of those cleared, 88 athletes were actually using the drugs? (Type a whole number.) The percentage of those cleared who were actually using the drugs is 0.50.5%. (Type an integer or decimal rounded to one decimal place as needed.)
The table below shows the batting records of two baseball players in the first half (first 81 games) and last half of a season. Answer parts a through d. player josh and jude Josh- first half 50 hits 150 at bats .333 batting average Second half 35 hits 70 at bats .500 batting avg. Jude 10 hits 50 at bats .200 avg 2nd 1/2 70 hits 150 at bat .467 avg
a. Which player had the higher batting average in the first half of the season? Josh
Write as a fraction in lowest terms. 0.68
17/25
According to the video, what is the conclusion of the argument? Choose the correct answer below. A. It's prohibited by law. B. Driving without a license is illegal. C. Driving without a license is unlawful. D. All of the above.
A. It's prohibited by law. B. Driving without a license is illegal. C. Driving without a license is unlawful.
Consider the following hypothetical basketball records for college A and college B. Answer parts a through c.
College A College B Home Games 10 wins, 19 losses 9 wins, 19 losses Away Games 12 wins, 4 losses 56 wins, 20 losses
Why are these two percentages different?
The percentages are different because people who test positive don't always have HIV and people who have HIV don't always test positive.
Find the scale ratio for the map described below. 1 cm(map)=500 mm (actual)
The scale ratio is 1 to 50000
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Even though your argument contains a fallacy, your conclusion is believable.
The statement makes sense. An argument that contains a fallacy can be believable.
Decide whether the following statement makes sense or does not make sense. Explain your reasoning. I drove at a speed of 35 miles for the entire trip. Choose the correct answer below.
The statement does not make sense because miles is not a unit of speed.
Which of the following best summarizes the strategic hint "There may be more than one strategy" and provides an example of the meaning?
There may be several strategies to solving a problem. However, not all of the strategies are equally efficient. For example, there is more than one strategy to solve x²+3x+2=0 however, using the quadratic formula involves more time and work.
What does the "Explain" step of this part of the problem solving approach?
The "Explain" step is to ensure that the result is reasonable.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Be sure to consider whether the units are appropriate to the statement, as well as whether the stated amount makes any sense. For example, a statement that someone is 15 feet tall uses the units (feet) appropriately, but does not make sense because no one is that tall. I know a professional bi-cyclist who weighs 210 kilograms.
This statement does not make sense because 210210 kilograms=463 pound(s), which is an unreasonable weight for a professional bicyclist.
Give an example of a problem that has more than one correct numerical answer.
Tommy bought 2 bags of chips and a box of cookies at the grocery store. He spent $6 total. How much does a bag of chips cost?
A monk set out from a monastery in the valley at dawn. He walked all day up a winding path, stopping for lunch and taking a nap along the way. At dusk he arrived at a temple on the mountaintop. The next day the monk made the return walk to the valley, leaving the temple at dawn, walking the same path for the entire day, and arriving at the monastery in the evening. Must there be at least one point along the path that the monk occupied at the same time of day on both the ascent and the descent?
Yes because there is one path, there must be a single spot that the monk occupied at the same time of the day on both the ascent and descent
The following table shows a housing index that can be used to compare housing prices in different cities. Suppose you see a house valued at $260,000 in City C. Find the price of a comparable house in City K, City A, and City D.
price. price x. index other town / other town = your town index your town A comparable house inCity K would cost about $541667 (Round to the nearest dollar.) A comparable house in City A would cost about $964167. (Round to the nearest dollar.) A comparable house in City D would cost about $877500. (Round to the nearest dollar.)
In the following argument, identify the premise(s) and conclusion, explain why the argument is deceptive, and identify the type of fallacy it represents. My little boy loves dolls and my little girl loves trucks, so there's no truth to the claim that boys are more interested in mechanical toys while girls prefer maternal toys. Identify the premise(s) and conclusion of the argument. Choose the correct answer below.
Premise: My little boy loves dolls and my little girl loves trucks. Conclusion: It's not true that little boys are more interested in mechanical toys and girls prefer maternal toys
Identify the type of fallacy the argument represents. Select all that apply.
hasty generalization appeal to ignorance
Compare A and B in three ways, where A=51093 is the number of deaths due to a deadly disease in the United States in 2005 and B=17946 is the number of deaths due to the same disease in the United States in 2009. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.
a. The ratio of A to B is 2.85 Type an integer or decimal rounded to two decimal places as needed. b. The ratio of B to A is .35. (Type an integer or decimal rounded to two decimal places as needed.) c. A is 285 percent of B. (Round to the nearest integer as needed.)
Do the following operations without a calculator. Be sure to express answers in scientific notation. You may round your answers to one decimal place as in 3.2x10^5.
a (2x10^5)x(2x10^3)=4x10*
What is the third way to use percentages?
Percentages can be used to compare two things. For example, the car costs 25% more but gets 10% more miles per gallon.
Why is the argument deceptive? Choose the correct answer below.
The lack of knowledge about the truth of a proposition is used as evidence against the proposition
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. In order to present a logical argument to Andrea, Julian had to shout at her.
The statement does not make sense. Shouting a logical argument does not improve the argument.
The Congressperson is a member of a national firearms club, so I'm sure she will not support a ban on rifles. Choose the type of fallacy the argument represents. Select all that apply.
straw man personal attack
For such a test, what is a true negative?
A true negative would be when an athlete that is not using a banned substance tests negative for banned substances.
Suppose you needed $0.21 to buy a particular box of macaroni and cheese in 1982. How much would it cost to buy the same box of macaroni and cheese in 2005? Assume that all prices have risen at the same rate as the CPI.\
How much would it cost? $.43 price in $y=(price in $y)x CPIy/CPIx X = year for which the price is KNOWN Y= price to be found
b. In "2016 constant dollars," the average domestic airfare for 1994 was $436. Does this mean that airfares rose more or less than expected with inflation based on the Consumer Price Index? Explain.
The actual 2016 airfare is less than it would have been if prices had risen with inflation.
Complete the following sentence. The gestation period of horses (336 days) is _____ percent longer than the gestation period of bears (220 days).
The gestation period of horses 336 days) is 52.75 percent longer than the gestation period of bears 220 days)
Convert the following fractions to decimal form.
3/5= 0.6 (Round to the nearest thousandth as needed.) 3/9=0.333 (Round to the nearest thousandth as needed.)
For such a test, what is a true positive?
A true positive would be when an athlete that is using a banned substance tests positive for banned substances.
Explain the apparent inconsistency in these results. Choose the correct answer below.
Although State A had lower scores in each category, it had a higher percentage of people in the higher scoring category, so the overall average is higher.
Could a person ride a bike across the United States Massachusetts to Washington State) in a month? If not, about how long would it take?
An estimate for how far a bicyclist can travel in a month is the product of the distance travelled per day, 40 miles per day, and the number of days per month 30. This results in an order of magnitude estimate of 1200 mi/mo, which is less than the distance from Massachusetts to Washington State, which is approximately 3000 miles. Therefore, a bicyclist cannot ride a bike across the United States in a month. It would take a bicyclist approximately 2.5 months to travel from Massachusetts to Washington State..
Use the data in the table below to determine how many average candy bars an adult would have to eat to five hours of running.
Energy released by metabolism of 1 average candy bar 1×106 Energy needed for 1 hour of running (adult) 3.9x10^6 The adult would have to eat 20 average candy bars. (Round to the nearest whole number as needed.)
3E Professional athletes are routinely barred from participation for using banned substances. Consider this scenario and answer the following questions.
For such a test, what is a false positive? A false positive would be when an athlete that is not using a banned substance tests positive for banned substances.
How are their meanings related?
If the compared value is P% more than the reference value, it is (100+P)% of the reference value.
Give an example that illustrates how a relative change is calculated. Choose the correct answer below.
If the new value is 50 and the reference value is 20, then relative change 50-20/20x100%=150%
Consider the following fallacy (which was not discussed in the text). Explain why the fallacy applies to the example. The slippery slope fallacy has the following form. Premise: X has occurred and is related to Y. Conclusion: Y will inevitably occur. Example: America has sent troops to three countries recently. Before you know it, we will have troops everywhere.
Let X be America sending troops to three countries recently. Let Y be America having troops everywhere. The two events are related, and Y will inevitably occur.
Give an example explaining how politicians on both sides of an issue can use numbers to support their case without lying.
Say a candidate is running for mayor of a city. During the incumbent mayor's first year in office, the city had a population of 25,000, and 50 violent crimes were committed. During the incumbent mayor's most recent year in office, the city had a population of 30,000, and 55 violent crimes were committed. The new candidate might argue that the number of crimes has increased, with 55 more crime(s) having been committed during the incumbent mayor's most recent year in office compared to the incumbent mayor's first year in office The incumbent might argue that the crime rate has decreased, with a rate of 1 violent crime for every 500 people during the incumbent mayor's first year in office and a rate of 1 violent crime for every 545 people during the incumbent mayor's most recent year in office. (Round to the nearest whole number as needed.)
woman bought a dining table dining table for $300 and then sold it for $900. She bought it back for $700 and then sold it again for $600. How much did she gain or lose on these transactions?
She gained $500. (Type a whole number.)
Explain how it is possible for a very accurate polygraph or drug test to result in a large proportion of false accusations.
Since the probabilities of both a false negative and a true negative are very low, the proportion of false negatives to total negatives will be large.
Find the absolute change and the relative change in the following case.
The absolute change describes the actual increase or decrease from a reference value to a new value. absolute change=new value−reference value=348−807=−459
Decide which of the two given prices is the better deal and explain why. You can fill a 1515-gallon tank of gas for $40.01 or buy gas for $2.70/gallon.
The better deal is to fill a 15-gallon tank for $40.01 because the price to fill a 15-gallon tank of gas for $40.01 is $2.67 per gallon.
Find the inflation rate from 1985 to 1986. Assume that all prices have risen at the same rate as the CPI.
The inflation rate was about 1.9%. The rate of inflation from one year to the next is the relative change in the Consumer Price Index. The relative change is the difference in the two CPI values divided by the initial CPI as shown, where X and Y represent years. CPIy-CPIx/CPIx x=initial year y= the final year CPI each year from the table
Explain the difference between the key words 'of' and 'more than' when dealing with percentages. How are their meanings related?
The key word 'more than' is used to express the relative change between the referenced value and the compared value. The key word 'of' is used to express the ratio of the compared value to the referenced value.
Explain how these results illustrate Simpson's paradox.
When the first and second halves of the season are taken separately, the data show that Josh is the better hitter in both halves. When the season is taken as a whole, the data show that Jude is the better hitter overall.
Convert each of the following numbers from scientific to ordinary notation, and write its name.
a 4x10^6=4,000,000=four million b 8.7x10^4=87000=eighty seven thousand c. 8x10^-2=.08=eight hundredths d. 4.1x10^-5=.000041 = forty-one millionths
b. A room has a rectangular floor that measures 27]feet by 13 feet and a flat 8-foot ceiling. What is the area of the floor and how much air does the room hold?
b. The area of the floor is 351 ft squared .ft2. (Type an integer or a decimal.) The amount of air the room can hold is 2808 ft cubed .
Explain why the speed of the Earth makes sense. Choose the correct answer below.
speed=distance/time=25,000 miles/24 hours
List three common units of energy. Under what circumstances do the different units tend to be used?
Kilowatt-hour; used to measure electrical energy for utility bills. Calorie; used to measure the energy the human body can draw from food. Joule; the international metric unit for energy.
200 in scientific notation is
2x10^2
There are approximately 3.2 million deaths per year in country A. Express this quantity as deaths per minute.
In country A, there are 6.1 deaths/min. 3200000 deaths/365*24*60min=8.2 deaths/min
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The price of tuition has tripled since my parents went to school—that's a 200% increase in price.
he statement makes sense. A 200% increase in price corresponds to a price that is 300% of the original price.
3B Explain how we can use estimation to put numbers in perspective. Give an example. Choose the correct answer below.
Estimation allows for values to be approximately calculated based on educated guesses and logical extrapolation. Estimation can be used to find the number of drinks consumed at football games in one year by multiplying the attendance per game with the drinks consumed per attendee, and then multiplying by the number of games per year; where each component value can be approximate.
Write out the three steps of the Understand-Solve-Explain process when answering the following question. How fast does Earth rotate? Note that in one full rotation of Earth, a point on the equator travels about 25,000 miles in 24 hours.
The speed
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I live in an apartment building that is 200 feet tall.
The statement makes sense because apartment buildings exist that are 200 feet tall.
Decide whether the following statement makes sense or does not make sense. Explain your reasoning. An 18th-century philosopher once said, "A penny saved is a penny earned," but if he were alive today, he would be talking about a dollar rather than a penny.
The statement makes sense. Due to inflation, a penny in the 18th century has about the same purchasing power as a dollar today.
Consider the following exam question and student solution. Determine whether the solution is correct. If it is not correct, write a note to the student explaining why it is wrong and give a correct solution. Exam question: You can buy a 34-pound bag of flour for $66 or you can buy a 1-pound bag for $0.39. Compare the per pound cost for the large and small bags. Student solution: The large bag price is 34÷$6=$5.67 per pound, which is much more than the39¢ per pound price of the small bag.
The student's solution is incorrect. The student's division gives an answer with units of pounds per dollar, but he should seek an answer in dollars per pound. The answer in dollars per pound is $. 18 per pound, which is less than the $0.39 per pound for the smaller bag. (Round to the nearest cent as needed.)
When interpreting a percentage problem using the words "more than" where the compared value is P% more than the reference value, the compared value is (100+P)% of the reference value.
(100 + 28%=128%
Which type of fallacy does the argument represent?
False Cause
The 2013 online library from the University of California at Los Angeles (UCLA) states "The World Wide Web has a lot to offer, but not all sources are equally valuable or reliable" (UCLA 2013). The online library suggests specific points to consider including evaluating the audience, determining the purpose of the information, completeness, comparing to other sources, and general critical thinking skills in determining if the information is credible. When evaluating a website for reliability, which of the following is not an item to consider?
Is the site visually appealing?
What is the Consumer Price Index (CPI)? How is it supposed to be related to inflation?
It is a way of measuring the prices consumers pay for products. It allows one to see how prices have changed with time, and therefore measures inflation.
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and, if possible, identify the type of fallacy it represents. My baby was vaccinated and later developed autism, which is why I believe that vaccines cause autism. Identify the premise. Choose the correct answer below.
My baby was vaccinated and later developed autism.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. We found that these rare cancers were 700% more common in children living near the toxic landfill than in the general population.
The statement makes sense because the number of rare cancers found in children living near the toxic landfill is 8 times the number of rare cancers found in the general population, which is possible.
Briefly describe the Understand-Solve-Explain approach to problem solving, giving examples of things that should be considered in each step. What is the "Understand" step of this part of the problem solving approach?
The "Understand" step is to think about what the problem asks to be determined.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
I've seen about 10 ^50 commercials on TV. The statement does not make sense. Put the number in perspective by thinking in terms of time. A TV commercial is about 1 minute long, so it would take 10^50 minutes to watch 10 ^50 commercials. 10^50minx1hr/60minx1day/24hrsx1yr/365days=1.9x10^44 years
Which of the following best summarizes the strategic hint "Consider equivalent problems with simpler solutions" and provides an example of the meaning?
A useful approach to a difficult problem is to look for an equivalent problem, which has the same numerical answer but may be easier to solve. For example, suppose you cannot remember the formula for surface area of a cube. Instead, find the surface area of each square and add them together.
Consider the following example of a fallacy. Complete parts a and b below. Fifty years of searching has not revealed life on other planets, so life in the universe must be confined to Earth. a. Identify the premise and conclusion of the argument. Choose the correct answer below.
Premise: Fifty years of searching has not revealed life on other planets. Conclusion: Life in the universe must be confined to Earth.
A certain race is a distance of 38 furlongs. How far is the race in (a) miles? (b) yards?
The race is 4.75 mile(s). The race is 8360 yard(s).
c. A grain silo has a circular base with an area of 155 square feet and is 23 feet tall. What is the total volume?
c. The volume of the grain silo is 3565 ft cubed .ft3. (Type an integer or a decimal.) Question is complete.
Consider the following example of the logical fallacy of circular reasoning. Complete parts (a) and (b) below. It's illegal to drive over the speed limit and breaking the law makes you a criminal, so people who exceed the speed limit are criminals. a. What is the premise? Choose the correct answer below.
It's illegal to drive over the speed limit.
Suppose you needed $22,000 to maintain a particular standard of living in 1974. How much would you have needed in 2001 to maintain the same standard of living? Assume that all prices have risen at the same rate as the CPI. How much would you have needed?
$79030 PRICE IN $y=(PRICE IN $x)X CPIy/CPIx
a. Verify that incidence rates for the general and "at risk" populations are 0.30.3% and 1010%, respectively. Also, verify that detection rates for the general and "at risk" populations are 95%. How would you verify the incidence rates?
A. Divide the number of infected patients by the total number of patients.
What is an order of magnitude? Explain why such an estimate can be useful even though it may be as much as 10 times too large or too small.
An order of magnitude estimate specifies only a broad range of values, usually within one or two powers of ten. These estimates are useful because they provide a way to easily tell the difference in groups of values, such as populations.
The Department of Health of a certain state estimates a 1010% rate of HIV for the "at risk" population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection of 5000 "at risk" people and 20,000 people from the general population results in the following table. Use the table below to complete parts (a) through (e).
At Risk" Population General Population Test Positive Test Negative Test Positive Test Negative Infected 470470 3030 5353 77 Not Infected 224224 42764276 997997 18 comma 943
Which of the following best summarizes the strategic hint "Use appropriate tools" and provides an example of the meaning?
Choosing only the tools most suited to the job will make tasks much easier. For example, if a problem can be solved one way with calculus and another way with multiplication, using multiplication will make the solving process easier.
b. Consider a patient in the "at risk" population. Of those with HIV, what percentage test positive? Of those who test positive, what percentage have HIV? Explain why these two percentages are different.
Of the patients in the "at risk" population with HIV, 94% test positive. Of the patients in the "at risk" population who test positive, 67.7% have HIV. (Type an integer or decimal rounded to the nearest tenth as needed.)
Decide which of the two given prices is better and explain why. Storage locker A rents for StartFraction $ 34/yd² per month. Storage locker B rents for $ 1.97/ ft² per week. Assume 1 month=4 weeks.)
Storage locker A is the better deal because after converting to the units of B's rental price the cost of locker A is $.94/ft² per week which is cheaper than B's rental cost of $1.97/ft²per week
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and, if possible, identify the type of fallacy it represents. Claims that fracking causes earthquakes are ridiculous. I live near an oil well and have never felt an earthquake.
The premise is I live near an oil well and have never felt an earthquake. The conclusion is claims that fracking causes earthquakes are ridiculous.
How much will a person pay for 14.7 pounds of bananas at a price of $2.41 per pound?
The price the person will pay is 35.43 dollars. (Round to the nearest cent.)
Suppose admission to a movie cost $7.00 in 2004. What was its price in 1987 dollars? Assume that all prices have risen at the same rate as the CPI.
The price was about $4.21 in 19871 (Round to the nearest cent.)
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. The price per gallon of gasoline has risen from only a quarter in 1918 to nearly $3 in 2009, thereby making it much more difficult for the poor to afford fuel for their cars.
The statement does not make sense because when inflation is taken into account, the two prices are quite comparable.
6 OF 15 Suppose that 8 turns of a wire are wrapped around a pipe with a length of 60 inches and a circumference of 4 inches, so that the wire reaches from the bottom of the pipe to the top. What is the length of the wire? (Hint: Picture cutting the pipe along its length and pressing it flat.)
The wire is 68 inches long.
Two candidates for governor of a state differ in their accounts of the state's economy during the incumbent's term. The incumbent claims that during his four-year term the economy has improved, citing a rise in the median household income from $33,000 to $34,500. The challenger claims that the economy has declined, citing that the buying power of families in the state has declined during the four years. Which of the following best explains how both candidates can be right?
Though the median household income increased, prices increased by a greater percent, meaning that in real terms the median income actually decreased.
The table to the right is based on the assumption that 1% of breast tumors are malignant. It also assumes that mammogram screening is 85% accurate. Complete parts (a) through (c) below.
a. Suppose a patient has a positive mammogram. What is the chance that she really has cancer? 7.17.1% (Type an integer or decimal rounded to the nearest tenth as needed.) b. What is the chance of a positive mammogram, given that the patient has cancer? 8585% (Type an integer or decimal rounded to the nearest tenth as needed.) c. Suppose a patient has a negative mammogram. What is the chance that she actually does have cancer? 0.170.17%
Now consider the table below that gives the actual percentages of males and females in each state. Use these percentages to verify that the overall average test score in state A is 267, as claimed in the first table. A 88% m 12%f B 66% m 34% f
Overall Test Score State Aequals=267 (Round to the nearest whole number as needed.)
Convert the measurement to the units specified. 16 pounds to kilograms
16 pounds = 7.26 kg.
Write each of the following as a common fraction. . The common fraction for 8.5 (Simplify your answer.)
17/2
Write as a fraction in lowest terms. .68
17/25
Convert the following quantities to the indicated units. 19 square kilometers to square miles
19 square kilometers=7.3 square mile(s)
c. Suppose a patient in the "at risk" category tests positive for the disease. As a doctor using this table, how would you describe the patient's chance of actually having the disease? Compare this figure to the overall rate of the disease in the "at risk" category
A patient in the "at risk" category who tests positive has a 67.7% chance of having the disease which is greater than the overall "at risk" incidence rate of 10%. (Type an integer or decimal rounded to the nearest tenth as needed.)
Total spending on health care in a certain region rose from $37 billion in 11978 to $1.1 trillion in 2006. Compare this rise in health care spending to the overall rate of inflation as measured by the Consumer Price Index.
Health care spending increased by 2873%. (Round to the nearest percent as needed.) The overall rate of inflation was 209%. (Round to the nearest percent as needed.)
Which of the following best summarizes the strategic hint "Approximations can be useful" and provides an example of the meaning?
Most real-world problems approximate numbers to begin with, so an approximation is often good enough for a final answer. Approximations also provide a useful check. For example, if a real-world problem involves long lengths with several decimals, approximating the final answer is often good enough for a final answer.
c. Is it true that the average speed for the round trip is the average of 6 miles per hour and 2 miles per hour (which iS 4.0 miles per hour)? (Hint: Did you spend more time traveling 6 miles per hour or 2 miles per hour?)
No, because less time is spent traveling 6 miles per hour.
continue with chapter 3a. Describe the three basic uses of percentages. Give a sample statement that uses percentages in each of the three ways. What is one way to use percentages?
Percentages can be used to express a fraction of something. For example, out of 15,000 employees, 3% lost their jobs.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. When we chart the price of milk in 1995 dollars we find that it has become slightly more expensive, but when we chart it in 1975 dollars we find that it has become cheaper.
The statement does not make sense because the same trend would be seen regardless of what kind of dollars are used.
2C Summarize the strategic hints for problem solving, and give an example of the meaning of each one. Which of the following best summarizes the strategic hint "There may be more than one answer" and provides an example of the meaning?
Some problems in mathematics have more than one answer. Without further information, there is no way to determine whether both solutions are valid for a particular problem. For example, both X=-2 ARE solutions to x²=4
Which of the following best summarizes the strategic hint "Consider simpler, similar problems" and provides an example of the meaning?
Sometimes, the insight gained from solving the easier problem may help to understand the original problem. For example, instead of picturing molecules mixing together, try to picture marbles mixing together.
Which state had the higher overall average across both categories?
State A
a. Which state had the higher scores in both categories?
State B
2B What are the basic metric units of length, mass, time, and volume? How are the metric prefixes used?
The basic metric units of length, mass, time, and volume are the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, and the liter (L) for volume. These basic units can be combined with a prefix that indicates multiplication by a power of 10.
A commuter train travel 33 miles in 28 minutes. What is its speed in miles per hour?
The speed is approximately 70.7 mi/hr (Round to the nearest tenth as needed.)
In making price comparisons, why is it important to adjust prices for the effects of inflation? Briefly describe how the CPI is used to adjust prices.
When comparing prices in different years inflation must be taken into account. Given a price in dollars for year ($y), the equivalent price in dollars for year Y ($y) is given by the formula shown below price in $y = price in $x * CPIy/CPIx
The following table shows deaths due to tuberculosis (TB) in City A and City B in a certain year. Complete parts (a) through (c) below.
a. Compute the death rates for whites, nonwhites, and all residents in City A. The death rate for whites is 0.18%. The death rate for nonwhites is 0.61%. The death rate for all residents is 0.19%. (Type integers or decimals rounded to the nearest hundredth as needed.) b. Compute the death rates for whites, nonwhites, and all residents in City B. The death rate for whites is 0.15%. The death rate for nonwhites is 0.34%. The death rate for all residents is . .22%. (Type integers or decimals rounded to the nearest hundredth as needed.) c. Explain the apparent inconsistency in these results. The death rate for both whites and nonwhites was higher in City A than in City B, yet the overall death rate was higher in City B than in City A. This is because the population percentage of nonwhites was significantly lower in City A than in City B.
Complete parts (a) through (c) below. a. A warehouse is 65 yards long, 32 yards wide, and 7 yards high. What is the area of the warehouse floor? If the warehouse is filled to half its height with tightly packed boxes, what is the volume of the boxes?
a. The area of the warehouse floor is 2080 yd squared . The volume of the boxes in the warehouse is 7280 yd cubed .yd3. (Type an integer or a decimal.)
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Be sure to consider whether the units are appropriate to the statement, as well as whether the stated amount makes any sense. For example, a statement that someone is 15 feet tall uses the units (feet) appropriately, but does not make sense because no one is that tall. I drank 1.3 liters of water today.
This statement makes sense because 1.3 liters=0.3 gallon(s), which is a reasonable amount of water to drink in one day.
Suppose you run 3 miles from your house to a friend's house at a speed of 6 miles per hour. When the time comes to return home, you are tired and walk the same 3 miles home at 2 miles per hour. Complete parts (a) through (d) below. a. How long did you spend running to your friend's house? (Type an integer or decimal rounded to the nearest tenth as needed.)
.5 HOURS
Briefly explain how circular reasoning occurs in the argument. Choose the correct answer below.
The conclusion is a restatement of the premise.
Use the table from part (c) to verify that the overall average test score in State B is 262, as claimed in the first table.
Overall Test Score State B=262 (Round to the nearest whole number as needed.)
Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting a pair of the same color?
3 socks. Suppose a brown sock is taken from the drawer. Then, a second sock is taken from the drawer, which is blue. A third sock is pulled, which is either brown or blue.
Distinguish between absolute and relative change. Give an example that illustrates how a relative change is calculated Distinguish between absolute and relative change. Choose the correct answer below.
Absolute change describes the actual increase or decrease from a reference value to a new value. Relative change is the size of the absolute change in comparison to the reference value and can be expressed as a percentage.
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. To figure out how long an airplane will take to reach Beijing, divide the distance to Beijing by the airplane's speed.
The statement makes sense because time is equal to distance divided speed.
What does the "Solve" step of this part of the problem solving approach?
The "Solve" step is to carry out the required steps and calculations.
The area of a certain country is 28% more than the area of California, so the country's area is what percent of California's area?
The country's area is 128% of California's area.
Write each of the following numbers in scientific notation.
a. 310=3.1 times 10 ^2 b 0.00617=6.17x10^-3 0.013122=1.3122x10^2
Find the absolute change and the relative change in the following case. The number of daily newspapers in a country decreased from 2648 in 1900 to 1341 in 2010.
The absolute change is -1307 (Simplify your answer. Type an integer or a decimal.) The relative change is −49%.
In the following statement, express the first number as a percentage of the second number. A certain candidate won 270 electoral votes in an election, out of a total of 407
The number of electoral votes won by the candidate is 66.3% of the total votes. (Round to the nearest tenth as needed.)
According to the video, http://mediaplayer.pearsoncmg.com/assets/UUM7B_1a_ex2 what is the conclusion?
The potato salad made me sick
In the following argument, identify the premise and conclusion, explain why the argument is deceptive, and, if possible, identify the type of fallacy it represents. I ate oysters for dinner and later that night I had a nightmare. Oysters caused my nightmare.
The premise is I ate oysters for dinner and later that night I had a nightmare. The conclusion is oysters caused my nightmare.
Why is the argument deceptive? Choose the correct answer below.
The premise tells us one thing happened before another, but doesn't prove any connection between them.
A commuter train travels 33 miles in 28 minutes. What is its speed in miles per hour?
The speed is approximately 70.7 mi / hr Round to the nearest tenth as needed.
